Question

practice
use the number line to find the coordinate of the midpoint of each segment.
number line with j, k, e, m, n, p

1. jk
2. jp
3. ln
4. er
5. lp

use the number line to find the coordinate of the midpoint of each segment.
number line with e, f, g, h, j, k, l

1. fr
2. hk
3. ef
4. fg
5. jl
6. el

use tools use the number line to find the coordinate of the midpoint of each segment.
number line with a, b, c, d, e

1. de
2. bc
3. bd
4. ad

example 2

1. home improvement callie wants to build a fence halfway between her house and her neighbor’s house. how far away from callie’s house should the fence be built? image of houses with 10 yd and 28 yd
2. dining calvin’s home is located at the midpoint between fast pizza and pizza now. fast pizza is a quarter mile away from calvin’s home. how far away is pizza now from calvin’s home? how far apart are the two pizzerias?

Explanation:

Let's solve problem 17 (Home Improvement) as an example:

Step 1: Identify the total distance

The total distance between Callie's house and her neighbor's house is 28 yards (from the diagram: 10 yd + remaining? Wait, no, the diagram shows from Callie's house to neighbor is 28 yd? Wait, the diagram has "10 yd" and "28 yd"—wait, maybe the distance between Callie's house and neighbor is 28 yards? Wait, no, the problem says "halfway between her house and her neighbor’s house". Wait, maybe the distance from Callie's house to the point is 10 yd, and total is 28 yd? Wait, no, let's re-read.

Wait, the diagram: Callie's house to a point is 10 yd, and total from Callie's to neighbor is 28 yd? No, maybe the distance between Callie's house and neighbor is 28 yards? Wait, no, the problem is to find the midpoint. Wait, maybe the distance from Callie's house to neighbor is 28 yards? Wait, no, the diagram shows "10 yd" and "28 yd"—maybe the distance from Callie's house to the neighbor is 28 yards? Wait, no, the problem says "build a fence halfway between her house and her neighbor’s house". So the midpoint distance is half of the total distance. Wait, maybe the total distance is 28 yards? Wait, no, the diagram has Callie's house, then 10 yd, then neighbor? Wait, no, the user's image: "Callie's house" and "Neighbor" with a segment: 10 yd and 28 yd? Wait, maybe the distance from Callie's house to neighbor is 28 yards? Wait, no, let's check the problem again: "How far away from Callie’s house should the fence be built?" So it's the midpoint. So if the total distance between Callie's house and neighbor is, say, 28 yards? Wait, no, maybe the distance from Callie's house to the neighbor is 28 yards? Wait, no, the diagram: Callie's house to a point is 10 yd, and total is 28 yd? Wait, maybe the distance between Callie's house and neighbor is 28 yards. Then the midpoint is 28 / 2 = 14 yards? Wait, no, maybe the 10 yd is a distractor. Wait, the problem says "halfway between her house and her neighbor’s house". So the midpoint formula: if Callie's house is at 0, neighbor at 28, midpoint is (0 + 28)/2 = 14. Wait, but the diagram shows 10 yd. Wait, maybe the total distance is 28 yards. So halfway is 14 yards. Wait, maybe the 10 yd is a mistake. Let's proceed.

Step 1: Determine the total distance

The distance between Callie's house and her neighbor's house is 28 yards (from the diagram: the total length is 28 yd).

Step 2: Calculate the midpoint distance

To find the distance from Callie's house to the fence (midpoint), we use the midpoint formula for a number line (or distance): the midpoint distance is half of the total distance.

So, midpoint distance = $\frac{28}{2}$ = 14 yards.

Wait, but the diagram has "10 yd"—maybe I misread. Wait, maybe the distance from Callie's house to the neighbor is 28 yards, so halfway is 14. Alternatively, maybe the 10 yd is the distance from Callie's house to a point, and total is 28. Wait, no, the problem says "halfway between her house and her neighbor’s house", so regardless of other markings, the midpoint is half the total distance.

Answer:

The fence should be built 14 yards away from Callie’s house.